To ease your problem, consider "L" as you x-axis Then the coordinate become: A(- 4 , 3) and B(1 , 2) [you notice that just the y's changed]
This is a reflection problem. Reflect point B across the river line "L" to get B', symmetric of B about L. The coordinates of B'(1 , -1) [remember L is our new x-axis] JOIN A to B' . AB' intersect L, say in H We have to find the shortest way such that AH + HB = shortest. But HB = HB' (symmetry about L) , then I can write instead of AH + HB →→ AH + HB'. This is the shortest since the shortest distance between 2 points is the straight line and H is the point requiered
